What’s Going On in This Graph? | Sept. 19, 2017

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By The Learning Network

Sept. 19, 2017

Updated: Sept. 23, 2017

Students

1. This is a graph that originally appeared elsewhere on NYTimes.com. For the purposes of this activity, we have removed some of the original text and features, all of which we will reveal later this week.

After looking closely at the diagram above (or at this full-size image), think about these three questions:

• What do you notice? • What do you wonder? • What’s going on in this graph?

The questions are intended to build on one another, so try to answer them in order.

2. Next, join the conversation by clicking on the comment button and posting in the box that opens on the right. (Students 13 and older are invited to comment, although teachers of younger students are welcome to post what their students have to say.)

3. After you have posted, try reading back to see what others have said, then respond to someone else by posting another comment. Use the “Reply” button or the @ symbol to address that student directly.

Each Tuesday, our collaborator, the American Statistical Association, will facilitate a discussion from 9 a.m. to 2 p.m. Eastern time by paraphrasing comments and linking to responses to help students’ understanding go deeper. You might use their responses as models for your own.

4. On Friday mornings, we will reveal at the bottom of this post a link to the original graph and the article that accompanied it. We’ll also provide related statistical nuggets that might help you more fully make sense of the graph. How does this new information influence your interpretation?

We threw you for a loop with the first “What’s Going On In This Graph?” It was modified from the map used in the Upshot article “Houston May Get 50 Inches of Rain. How Long Does It Take Your City to Get That Much?” It wasn’t a typical graph with bars or points, but a map. The map shows precipitation — a variable — with its geographic location. A map adds location — another variable, which can’t be shown in a graph. Below in Stat Nuggets, we explain how some maps can be graphs. For every “What’s Going On In This Graph?”, Stat Nuggets will have a few statistical terms related to that particular graph. We’ll define the terms and give examples from that month’s graph.

The article had a personalized, interactive feature inviting you to enter your city or ZIP code. Then, it compared the number of months it would take in your area in the past to get Houston’s 50 inches of rain that fell in one week. Surprised at the response for your area?

In your comments, there was lots of strong critical thinking about what story this graph is telling. Many of you thought it showed something about 50 inches of precipitation for areas around the country. Some wrote about water levels, hurricanes and amount of damage. But, the tip off was the lead-in sentence — “By the time Hurricane Harvey left Texas, parts of Houston have been inundated by more than 50 inches of rain.” Combine that with the legend which ranged from 0 months to 5 years, and you have a graph of the amount of time that it would take for 50 inches of precipitation to fall by region.

But, there is more to this graph than that. Here are some wonderings that get into the graph’s deeper story.

• How was the precipitation statistic calculated? An average of some time period — a year, a decade? Looking at the article and, in particular, the interactive feature, can you figure out how the statistic was calculated?• A map shows land area, but it does not show how the population is distributed. What proportion of the country’s land area gets lots of precipitation? What percentage of the country’s population gets lots of precipitation? How do these percentages compare?• Take a look at the legend — 0 months to 5 years. Are the color intervals ordered? Time periods equal? How does your answer affect how you read the graph?• Compare the different parts of the country that get more precipitation to those with less precipitation. Base your comparison on such factors as the regions’ economic sectors, population growth, employment and wealth. Is the amount of participation associated with any of these factors? If yes, wonder why this may be so.• How does this map relate to where hurricanes occur? What else increases precipitation?

Thank you for being part of “What’s Going On In This Graph?”, intended to have you think more critically about graphs and the underlying data in a news story. As reflected in the questions above, critical thinking is an essential element of statistics, the science of learning from data. Further, data visualization is an important way statisticians and others work to understand and communicate about data.

Keep noticing and wondering. Come up with conjectures based on this graph. Probe whether they are possibly true, and if not, change your conjecture. You may continue to comment on other people’s posts.

We hope to see you again next month on Tuesday, October 10 for our next “What’s Going On In This Graph?”

Stat Nuggets for “50 Inches of Rain”

MAP as Graph

A map can be a graph when the map shows statistics with their geographic relationship.

In “50 Inches of Rain,” the map visually displays the precipitation by geographic area of the United States. The precipitation is a statistic calculated from rainfall data. These statistics could be represented in a chart, with columns for location and inches of rain. The statistics can be turned into a histogram, with number of months to get 50 inches of precipitation on the x-axis and acres getting that amount of precipitation on the y-axis. Alternatively, they can be turned into a map, showing the geographic relationship of amount of rain precipitation.

STATISTIC

Statistics are numerical summaries of data.

In “50 Inches of Rain,” the statistic is the length of time for 50 inches of precipitation, based on rainfall data by region.

VARIABLE

A variable is a characteristic of the cases (individual units, such as people, states or anything we are studying) in the group of interest.

In “50 Inches of Rain,” the cases are regions of the United States. The variable is length of time for 50 inches of precipitation in each region.

QUANTITATIVE Variable

Quantitative variables have a number as a response. They have units and can be ordered. Taking the average of their responses makes sense. Alternatively, there are categorical variables, like favorite color, which don’t meet these criteria.

In “50 Inches of Rain,” the length of time for 50 inches of precipitation is a quantitative variable, which can be measured. It measures time and the units are months and years. Order exists as seen in the colored bar legend — four months is less than eight months. It makes sense to calculate and use the average length of time for 50 inches of rainfall for the United States.

_________

The graphs for “What’s Going On in This Graph?” are selected in partnership with Sharon Hessney, the Statistics Content Director at Mass Insight Education. In addition, Ms. Hessney and Corey Andreasen, a mathematics teacher at Qatar Academy Doha in Doha, Qatar, moderated the Tuesday comments and wrote this week’s “reveal” and Stat Nuggets section.